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Math Help - Factoring

  1. #1
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    Factoring

    Can someone show me why

    (a - b) ^2 - (c + d)^2 = (a-b-c-d)(a-b+c+d)
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  2. #2
    Senior Member eumyang's Avatar
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    Use the difference of two squares pattern:
    x^2 - y^2 = (x - y)(x + y)

    Substitute "a - b" for x and "c + d" for y:
    \begin{aligned}<br />
(a - b)^2 - (c + d)^2 &= [(a - b) - (c + d)][(a - b) + (c + d)] \\<br />
&= (a - b - c - d)(a - b + c + d)<br />
\end{aligned}
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  3. #3
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    skeeter's Avatar
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    Quote Originally Posted by Alan306090 View Post
    Can someone show me why

    (a - b) ^2 - (c + d)^2 = (a-b-c-d)(a-b+c+d)
    let (a-b) = x and (c+d) = y

    working from the right side ...

    (a-b-c-d)(a-b+c+d) =

    [(a-b)-(c+d)][(a-b)+(c+d)] =

    [x-y][x+y] =

    x^2-y^2 =

    (a-b)^2 - (c+d)^2
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